Question

Find a sum of all numbers made by permutation of 1,2,3,4,5 and 6.

Answer 1

I'll give you a clue: What you DON'T want to do is find all the permutations, write them down, then sum them.

Answer 2

hey, there are 6! of six-digit numbers ( 720 numbers ). The point is not to find a sum, but to find an easy way to find that sum.

Answer 3

That's what I was getting at (i.e. look for an easy way, do not do it). So you know there are 720 permutations - that's a good start.

What can you say about the number that have "1" in the first position? What about "2"? What about the numbers in the next position? Think along those lines.

Answer 4

5!

Answer 5

also, what does a '1', '3' etc in the first position mean (as opposed to, in the last)

Answer 6

5! of all those numbers - 6*5!

Answer 7

The answer is not going to be 5!. 5! is 120, which is a lot less than any permutation of of 123456 (assuming I understand the question right)

Answer 8

Sorry, I misunderstood you.

Answer 9

:)

Answer 10

Yes, 5! have each number is each position.

Answer 11

do u know how to do this ? I did something. i would like to write answer and u will have just to tell me if it's good. ok?

Answer 12

I do not know the answer, but I know how to work it out. I'll work it out now if you want

Answer 13

Yes, I want :) Thank u :)

Answer 14

Newton, I wrote a reply to your post under my previous post. Check it once you are done with this. And yes, I mean every word I say therem and you should carefuly rethink your life and actions, and PRIDE.

Answer 15

I did i on this way:
5!(100000 + (2+3+4+5+6)*10000 + (2+3+4+5+6)*1000 + (2+3+4+5+6)*100 + (2+3+4+5+6)*10 + (2+3+4+5+6)) +
5!(200000 + (1+3+4+5+6)*10000 + (1+3+4+5+6)*1000 + (1+3+4+5+6)*100 + (1+3+4+5+6)*10 + (1+3+4+5+6)) +
5!(300000 + (1+2+4+5+6)*10000 + (1+2+4+5+6)*1000 + (1+2+4+5+6)*100 + (1+2+4+5+6)*10 + (1+2+4+5+6)) +
5!(400000 + (1+2+3+5+6)*10000 + (1+2+3+5+6)*1000 + (1+2+3+5+6)*100 + (1+2+3+5+6)*10 + (1+2+3+5+6)) +
5!(500000 + (1+2+3+4+6)*10000 + (1+2+3+4+6)*1000 + (1+2+3+4+6)*100 + (1+2+3+4+6)*10 + (1+2+3+4+6)) +
5!(600000 + (1+2+3+4+5)*10000 + (1+2+3+4+5)*1000 + (1+2+3+4+5)*100 + (1+2+3+4+5)*10 + (1+2+3+4+5))

Answer 16

Erm, do you know what that comes out to in total? I did pretty much the same, but did it all in one go, rather than splitting the 100000s etc form the rest

Answer 17

1+2+3+4+5+6 = 21

Sum = 21 * 120 + 210 + 120 + 2100 * 120 ...... + ..... + 2100000 * 120
= 120 * 21 * 111111 = ....

Answer 18

sorry, the second line has a typo:

it should be 21 * 120 + 21 * 10 * 120 + 21 * 100 * 120 .... + ..... + 21 * 100000 + 120

Answer 19

The last + should be * , too ¬_¬ Sorry, I'm tired.

Answer 20

Thank u. I need more time to think about this :)